Each time an i term is produced, a machine has a 0.5% probability of it being de

Question

Each time an i term is produced, a machine has a 0.5% probability of it being defective. Each day, the machine is run until a defective item is produced and then it undergoes an extensive adjustment which requires the rest of the working day. (Geometric) 2. a. What 2 assumptions do we make? b. What may make these assumptions unrealistic for our situation? c. What is the average number of usable items that will be produced in one day? d. Find the probability that a machine will produce fewer than 200 usable items on a given day e. For the 250 working days of a year, what is the total number of usable items that will be produced on average? (use your answer from c. and a property of expectation)

Explanation / Answer

2.

a) Below are the assumption for Geometric distribution

1. The phenomenon being modelled is a sequence of independent trials.
2. There are only two possible outcomes for each trial, often designated success or failure.
3. The probability of success, p, is the same for every trial.

b)

Independence may not hold good in our situation.

c)

Expected number of failures before success i.e. occurrance of first defective item = (1-p)/p = (1-0.005)/0.005 = 199

d)

P(X<200) = 1 - (1-p)^199 = 1 - (1-0.005)^199 = 0.6312

e)

total number of usable items = 250*199 = 49750

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.